A339147 a(1) = 1; a(n) = max (A000005(n-1) , A000005(a(n-1))) , for n > 1.

1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 4, 3, 6, 4, 4, 4, 5, 2, 6, 4, 6, 4, 4, 3, 8, 4, 4, 4, 6, 4, 8, 4, 6, 4, 4, 4, 9, 3, 4, 4, 8, 4, 8, 4, 6, 6, 4, 3, 10, 4, 6, 4, 6, 4, 8, 4, 8, 4, 4, 3, 12, 6, 4, 6, 7, 4, 8, 4, 6, 4, 8, 4, 12, 6, 4, 6, 6, 4, 8, 4, 10

Offset

1,3

Comments

Empirically a(n) > A000005(n-1) for (n-1) = p, p >= 19 and for (n-1) = q^2, q >= 5; p, q primes. Also a(n) > A000005(n-1) for semiprimes (n-1) = r*s from {85,91,133,141,161,201,205,217,221,235,253,265,295,301,309,341,343,365,382,...}; r,s different primes.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Example

a(1) = 1; a(2) = max (A000005(1), A000005(1)) = 1; a(3) = max(A000005(2), A000005(1)) = 2; a(4) = max(A000005(3), A000005(2)) = 2; and so on.

Mathematica

Module[{n=1}, NestList[Max[DivisorSigma[0, n++], DivisorSigma[0, #]]&, 1, 100]] (* Paolo Xausa, Dec 10 2023 *)

Prog

(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = max(numdiv(n-1), numdiv(va[n-1])); ); va; } \\ Michel Marcus, Nov 29 2020

Crossrefs

Cf. A000005.

Sequence in context: A339666 A318881 A280338 * A062821 A353862 A338719

Adjacent sequences: A339144 A339145 A339146 * A339148 A339149 A339150

Keyword

nonn

Author

Ctibor O. Zizka, Nov 25 2020

Status

approved